Publication: Ultrametric spaces, valued and semivalued groups arising from the theory of shape
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2012
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UCM
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Abstract
In this paper we construct many generalizad ultrametrics in the sets of shape morphisms between topological spaes. We recognize a topology in these sets which is independen on the shape representation of the spaces. We construct valuations an semivaluations on groups of shape equivalences and on n-th shape groups. We also connect shape theory, for arbitrary topological spaces, with the algebraic theory of generalized ultrametric spaces developed by S. Priess-Crampe and P. Ribenboim among other authors.